What should should mean - Copley, Bridget.pdf

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What should should mean?

Bridget CopleyCNRS/Universite Paris 8

January 3, 2006

Abstract

One analysis of non-deontic should treats it as having less-than-universal quantification over the epistemically accessible worlds theworlds that, for all the speaker knows, could be the actual world. Thisanalysis is based on the intuition that should assertions are weakerthan are assertions of epistemic must sentences. Problems with thetraditional analysis, however, indicate that there must be a differentreason why these should sentences express weaker propositions. Thispaper argues that non-deontic should can involve either epistemic ormetaphysical modality; both are weaker than epistemic must because

shoulddoes not trigger a presupposition that things work out normally,while must does. An initially problematic attempt to extend thisanalysis to deontic should prompts a revision to Kratzers theory ofmodals, in which the division of labor between the modal base andthe ordering source is rethought.

1 The traditional view

English should, like many other modals, has more than one flavor of modalmeaning, as demonstrated by the examples in (1). (1a) conveys the speakers

assessment that the hearer would do well do go to school tomorrow. (1b)conveys the speakers assessment that it will likely rain tomorrow.

I am indebted to Nathan Klinedinst for helping me to realize a number of consequencesof my initial idea. Thanks as well to attendees of the Language Under Uncertainty work-shop for much helpful discussion, and to everyone who (advertently or inadvertently)provided me with data. All errors and omissions are mine.

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(1) a. You should go to school tomorrow.

b. It should rain tomorrow.

The same sentence can have both kinds of readings, as in (2), with twoparaphrases given in (2a) and (2b):

(2) Jenny should be there tomorrow.

a. If she wants to get the job, she really needs to be there tomorrow.b. Thats what I gather from what I know about her plans.

In each paraphrase, there are different kinds of facts that are presented asrelevant. In (2a), as in (1a), the relevant information seems to be about ideals

of some kind: either there is a rule saying what the ideals are, or there is ineffect a rule about what one would ideally do if one had certain ideals. Thiskind of reading is often referred to as a deontic or practical necessityreading. We will leave this reading aside until the very end of the paper, andinstead concentrate on the kind of reading exemplified in (1b) and (2b).

In these examples, the relevant information that the speaker takes intoconsideration seems to consist of facts about the world; the speakers evidenceor grounds for believing the proposition to be true. This kind of reading iscommonly known as the epistemic or logical necessity reading of shouldsentences.

Behind the choice of the term epistemic is the suspicion that the kind ofmodality involved has to do with speaker knowledge. That is, it is the samekind of modality that is involved in epistemic readings of must sentences asin (3) (the parenthetical in (3) is intended to rule out the deontic reading ofmust, on which Xander is required to be there).

(3) Xander must be there (his car is outside, his lights are on, etc.).

The starting idea is that the epistemic reading of a sentence must p says thatall epistemically accessible worlds are p worlds (Kratzer, 1991). Let C be acontext of utterance, an n-tuple including (at least) the speaker, the time of

utterance, and the world of utterance.(4) C := xC, tC, wCLet EC be the epistemically accessible set of worlds, the worlds that for allthe speaker knows could be the actual world:

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(5)

EC := the set of worlds compatible with what xC knows at tC in world

wC.

And let All be a function with the usual (Barwise and Cooper-inspired)semantics as follows:

(6) All := p q . p q = pWe can assume then that the meaning of must is as given in (7); it says of aproposition that it is true in all the worlds that are epistemically accessibleto the speaker at the world and time of speech.1

(7) [[must]](C)(p) := 1 iff All(

EC)(p)

Actually, as Kratzer points out, this denotation is too strong; it predicts thatthe proposition expressed by must p entails the one expressed by p, since theactual world has to be among the set of epistemically accessible worlds. Thesolution (following Lewis (1968, 1975)) is to say that the set quantified overis not the set of epistemically accessible worlds, but a subset of those worlds;the set of best epistemicallly accessible worlds according to some plausibilitymetric (or ordering source, in Kratzers terminology). Let us suppose thatwe can construct a function, relativized to the context C, that takes a setof worlds as its argument and returns the subset that contains exactly the

worlds in which the least out-of-the-ordinary things happen. We will be coyfor the moment about precisely how to construct this function.2 We changethe denotation of must to reflect this new set:

(8) [[must]](C)(p) := 1 iff All(highest-plausibilityC(EC))(p)Then, since it need not be true that the actual world is one of the mostplausible epistemically accessible worlds, must p is weaker than p, as desired.

Can this epistemic analysis be extended to non-deontic should? If so,how? Horn (1989) proposes that should is to must as most is to all, based onthe contrast shown in (9).

(9) a. #Xander must be there, in fact, he should be.

1For our purposes we are abstracting away from the temporal dimension; propositionsare sets of worlds, and p is true in w is the same as w is an element of p.

2For instance, at this point our context will have to contain more than what we haveput in it so far.

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b. Xander should be there, in fact, he must be.

Horn argues that the contrast in (9) shows that a should sentence expressesa weaker proposition than its must counterpart. The argument is based ona Gricean implicature: the proposition expressed by the second clause mustnot be entailed by that expressed by the first, or else the Be informativemaxim would be violated. Horn argues that what goes wrong in (9a) isexactly that: The proposition expressed by he should be is entailed by theproposition expressed by Xander must be there.

This is exactly parallel to the behavior of all and most.

(10) a. #I ate all of the raisins, in fact, I ate most of them.

b. I ate most of the raisins, in fact, I ate all of them.

Horn argues that this weakness is due to a weaker quantifier in should. Andit is parallel to most, not, for instance, some, assuming that something likemay corresponds to some, as shown by (11) and (12).

(11) a. #I ate most of the raisins, in fact, I ate some of them.b. I ate some of the raisins, in fact, I ate most of them.

(12) a. #Xander should be there, in fact, he may be there.b. Xander may be there, in fact, he should be there.

To express the desired analysis of should, reflecting Horns idea in combina-tion with our Kratzer-style modal semantics, we define a function Most withthe usual semantics:

(13) Most := p q . | p q | > | p - q |And we give a denotation for shouldthat is true if on most of the epistemicallyaccessible worlds, p.

(14) [[should]](C)(p) := 1 iff Most((highest-plausibilityC(EC))(p)This analysis of should I will call the traditional view.

2 Evaluating the traditional view

As it turns out, the traditional view does not adequately account for themeaning of should.

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Unlike must p sentences, should p sentences are possible with a continu-

ation expressing the speakers absolute ignorance as to whether p is true ornot. This contrast is shown in (15).

(15) a. #The beer must be cold by now, but I have absolutely no ideawhether it is.

b. The beer should be cold by now, but I have absolutely no ideawhether it is.

The judgment for must in (15a) makes sense on the traditional view; if youuse must, and thereby convey that on all of the most plausible epistemicallypossible worlds the beer is cold, it would be strange to then comment that

you have no idea whether it is or not, giving rise to an instance of MooresParadox.3

The question is why the sentence in (15b) is not also an instance ofMoores Paradox. By the traditional view of should, the speaker is conveyingthat on most of the most plausible epistemically accessible worlds, the beeris cold. So if you utter (15b), there must be some reason why most of yourmost plausible epistemically accessible worlds are p-worlds. Perhaps you sawsomeone put the beer in the fridge. But the fact that there is some reasonthat the beer is cold on most of the worlds you are considering, is reasonenough why you should not be able to assert that you have absolutely no

idea if it is cold or not. You do have some idea.The problem is even worse, however: its not just that the speaker cancontinue that they have no idea whether p, but they can continue by assertingthat not-p is true (thus entailing, for our purposes, that p is false).

(16) a. #The beer must be cold by now, but it isnt.b. The beer should be cold by now, but it isnt.

Again, must behaves as expected. If on all the most plausible worlds thatfor all the speaker knows, could be the actual world, the beer is cold, it is aninstance of Moores Paradox for the speaker to then assert that the beer is

actually not cold. Should, however, again behaves unexpectedly. It would bestrange for the speaker to assert that on most of the most plausible worldsthat for all they know could be the actual world, the beer is cold, but that inthe actual world it isnt. If the speaker knows that the beer isnt cold, there

3Moores Paradox is, in its simplest form, the fact that the sentence p but I dont believethat p is contradictory.

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is no way they can assert that on most of the worlds that for all they know

could be the actual world, it is cold now.A possible objection might be that really we should be using dynamic

semantics; the context might be getting changed. After all, (17) (i.e., (16b)with the conjuncts switched), is decidedly odd, so dynamic semantics maywell be relevant.

(17) #?The beer isnt cold, but it should be.

The hope is that perhaps dynamic semantics could save the traditionalview from (16b). A dynamic semantics story for (17) would proceed roughlyas follows. The meaning of but requires that we update a context first with

the proposition that the beer is not cold, and then update that context withthe proposition that it should be. However, if should p has the traditionalmeaning, that on most of the most plausible epistemically accessible worlds,p, then it is not informative to update with should p, so (17) sounds strange.4

Now for the contrast in (16). For the must sentence in (16a), the con-text is first updated with the proposition that on all of the most plausibleepistemically accessible worlds, the beer is cold. Then it is not possible toupdate the context with the proposition that the beer is not cold. If, on theother hand, we are merely uttering the should sentence in (16b), there is noproblem; first the context is updated with the proposition that on most of

the most plausible epistemically accessible worlds, the beer is cold; and thenthe context is updated with the proposition that on the actual world the beeris not in fact cold.

Note that this explanation hinges on the idea that (16a) is bad exactlybecause must involves universal quantification. Less than universal quantifi-cation should pose no problem. However, consider (18).

(18) #The beer may be cold, but it isnt.

The sentence in (18) ought to be felicitous, as the treatment of (18) oughtto be similar to that of (16b). We ought to be able to update the context

first with the proposition that on some of the most plausible epistemicallyaccessible worlds, the beer is cold, and then with the proposition that thebeer is not actually cold. But (18) is not felicitous. If we believe that may is

4There also seems to be a problem with a presupposition of but of contrast, but thesame issue arises with and: The beer should be cold, and it isnt is much better than #?Thebeer isnt cold, but it should be.

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epistemic, this is a problem for the traditional view of epistemic should, be-

cause the less-than-universal-quantification explanation for the acceptabilityof (16b) cannot be correct.5

It seems an inescapable conclusion that while both mustand mayprecludethe speakers having knowledge about whether p holds of the actual world,should does not. Why is this so? And what, if anything, does the answerto this question have to do with the reason why should is somehow lessinformative than must?

Let us retrace our steps. Recall the initial evidence in (9), repeated belowas (19), that a shouldsentence is less informative than the corresponding mustsentence.

(19) a. The beer should be cold; in fact, it MUST be.b. #The beer must be cold; in fact, it SHOULD be.

The traditional view, we saw, attributes this property to should having aweaker force of quantification than must, though with both of them quan-tifying over (the most plausible) epistemically accessible worlds. However,this analysis was shown to wrongly predict that should triggers a version ofMoores paradox, which is not the case.

What could be done to make should weaker, aside from giving it a lessthan universal force of quantification? Let us return to the denotation we

gave for must in (7) above, repeated below as (20).(20) [[must]](C)(p) = 1 iff All(highest-plausibilityC(EC))(p)The denotation of must suggests two ideas for how to proceed. The firstidea is that perhaps should constrains the context less than must does, bypresupposing less. In that case, a must sentence would be more informativethan a should sentence because it would narrow down the context more.Another idea is that should does not quantify over the same set of worlds asmust does; instead it quantifies over a differently-constructed set of worldsthat happens to be smaller than highest-plausibilityC(EC). In that case,a must sentence would be more informative for reasons that would have todo with the relation between highest-plausibilityC(EC) and whatever thisother set of worlds was.

5The story is the same for a story in which epistemic modality is defined in terms ofthe outcome of updating the context in various ways (as in Veltman (1996) and Beaver(2001)). The idea is that there is no problem updating the information state for (17).

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Only one of these would have to be true to ensure that must sentences are

more informative than should sentences. In what follows, I will argue thatthe first idea is correct: mustsentences presuppose that the actual world willturn out to be among the highest-plausibility worlds, while should sentencesonly presuppose that it is possible for the actual world to turn out to be sucha world. This difference, along an axis we shall call efficacy, is responsiblefor the fact that should sentences are less informative than must sentences.

But the second idea, that should quantifies over a different set of worldsthan does must, also has a role to play. I will argue that some examples ofwhat has been called epistemic should actually quantify over metaphysi-cally accessible worlds. While a reading of should that quantifies over epis-

temically accessible worlds does exist, it appears to be marked typically byan different pattern of focus. Since it is not clear that the set of metaphysi-cally accessible worlds has any relation to the set of epistemically accessibleworlds, this idea does not do the job of making should weaker than must, butit is worth sorting out the facts.

As a postscript, of course shouldhas also the deontic or practical necessityreading as well; extending the theory to account for this reading of shouldwill motivate a change to Kratzers theory of modals.

First, however, let us take a closer look at the intuitions regarding epis-temic should, to argue that the first idea is correct: should presupposes lessthan must. The conclusion we will come to is that these modals differ in thepresupposition that they make about whether the expected course of eventswill actually come to pass. This axis we will call efficacy, since it reflectswhether the things that are supposed to happen actually manage to happen.

3 Efficacy

So, what has been said about non-deontic readings of should? Leech (1971),for one, takes logical necessity should to indicate that the speaker hasdoubts about the soundness of his/her conclusion. To illustrate the differ-

ence between should and must, he provides the following contrasting glossesfor the minimal pair of sentences in (21).

(21) Leech p. 101

a. Our guests must be home by now.(I conclude that they are, in that they left half-an-hour ago,

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have a fast car, and live only a few miles away.)

b. Our guests should be home by now.(I conclude that they are, in that . . ., but whether my conclusionis right or not I dont know its possible they had a breakdown,for instance.)

What is enlightening about this example is the particular flavor of doubtthat surfaces in the gloss of (21b). Its not that the speaker doubts their owninference from the facts to the conclusion, all else being equal; its that theydoubt that all else really will be equal. The relevant intuition seems to bethat should sentences say what ought to happen if things proceed normally,whatever normally means; this is our highest plausibility condition, andalso Kratzers ordering source. So it seems that must p presupposes thatthe actual world is going to be one of the most plausible worlds, while shouldp, if it presupposes anything, presupposes merely that it is (still) possiblethat the actual world is (going to turn out to be) one of the favored worlds.

How can we model this intuition about the difference between must andshould? What wed like is for must to require that the actual world bein the set highest-plausibilityC(EC), while should requires only that theactual world could be in that set. While the requirement for must is sen-sical, the requirement for should is non-sensical, in the current framework.What does it mean for a world to not be in that set, but possibly be in

it? Set membership is an in or out affair. What we are looking for seemsto be not a relationship between a world and a set of worlds, but betweentwo sets of worlds, which would provide the needed flexibility. That is, weare looking for a mystery set such that must requires it to be a sub-set of highest-plausibilityC(EC), while should requires only that andhighest-plausibilityC(EC) have a non-empty intersection. This gets uscloser, because it gives us a sense in which a world could be in highest-plausibilityC(E). If is a subset of highest-plausibilityC(E) any worldin must be in highest-plausibilityC(E). However, if is merely requiredto have a non-empty intersection with highest-plausibilityC(E), then anarbitrary world in might be in highest-plausibilityC(E), or it might not.(22) a. presupposition ofmust: highest-plausibilityC(EC)

b. presupposition ofshould: highest-plausibilityC(EC) = What could play the role of the mystery set ? Remember the intuition:

We want must and should to convey, via (22a) and (22b), whether the ac-

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tual world turns out to be one of the most plausible epistemically accessible

worlds. So perhaps an appropriate would be a set of worlds that are epis-temically accessible in a later context: a set just like EC, but with a different(later) context. We can call these sets epistemic states for short.

In that case, the presupposition of mustshould say that a later epistemicstate is a subset of the most plausible epistemically accessible worlds. Thatis not yet quite right; notice that the speaker of a must p sentence need notbelieve that they will get enough information to ever learn the truth, since(23) is non-contradictory.

(23) The murderer must have thrown the murder weapon into the Seine,but well never find it.

So it seems we need to say something a bit weaker: that any more informativeepistemic state (we assume that any later epistemic state is more informative)is a subset of the best (currently) epistemically accessible worlds. What itmeans for a later epistemic state to be more informative is that it rulesout more possible worlds; it is necessarily a subset of the current epistemicstate. However, in general, a later epistemic state need not be a subset ofthe set of most plausible worlds in the current epistemic state. The proposedpresupposition for must adds exactly that requirement. Thus:

(24) for all C, p:

a. [[must]](C)(p) asserts that highest-plausibilityC(EC) p, andpresupposes that Emore informative than EC:E highest-plausibilityC(EC)

b. [[should]](C)(p) asserts that highest-plausibilityC(EC) p,and presupposes that Emore informative than EC:Ehighest-plausibilityC(EC) =

This difference6 ensures that Moores Paradox does obtain for must p,but does not obtain for should p. If one asserts must p, one is committedto the idea that any more informative epistemic state is a subset of the set

of most plausible worlds, as well as the proposition that the most plausiblecurrently accessible worlds are a subset of the set p worlds. Therefore itis contradictory to continue by saying that you do not believe that a more

6See Copley (2002) for arguments that will, and future modals in general, have a similarpresupposition. Werner (2005) also refers to it.

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informative epistemic state will not be a subset of the set of p worlds. Since

should p does not presuppose that any more informative state is a subset ofthe set of most plausible worlds, this contradiction does not arise for shouldp utterances.

Does this solve the problem of the weakness of should? It does, becauseshoulds presupposition is weaker than musts.

If this is all correct, we are done.

4 Metaphysical and epistemic modality

So, is it all correct? Seemingly. We have epistemic analyses of both must

and should, explaining why should p is weaker than must p, also keepingmust p weaker than p. But as it turns out, we have not yet accounted forthe meaning of should, as we will see now.

Suppose you are indoors, and a friend who has been outside has just toldyou that, although it is not raining, the ground is wet outside. It would beentirely appropriate for you to utter the sentence in (25a) as a response. Itwould not, however, be appropriate to utter the sentence in (25b) (assumingthat the only grounds for asserting it was what your friend had just toldyou).

(25) a. It must have rained.b. #It should have rained.

This difference between must and should cannot be explained by a differencein efficacy, i.e. whether or not the actual world turns out to be one of the bestworlds. The reason is that the difference between (25a) and (25b) involves thetime at which evidence can be admitted. While (25a) admits evidence of theresults of the rain event, (25b) does not. The only way you can utter (25b)is if you have evidence about what the world was like before the (putative)rain event. If, for instance, you know that the clouds had been building up,and that a thunderstorm had been approaching, then you would be able to

say (25b). But the knowledge (or belief) that the ground is now wet is notrelevant.

Note as well that it is not a matter of past knowledge, either. You couldfelicitously say (25b) even if in the past, before the putative rain event, youdidnt know that the thunderstorm was approaching. It seems that thatthere are two differences between the inference evoked by must have and the

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inference invoked by should have. While must have reasons backwards from

current evidence, or our knowledge about it, should havereasons forward fromearlier events. And while must havereasons from what is known, should havereasons not from what was known in the past, but what was actually the casein the past.

So there are two differences: the direction of reasoning from the evidence,and the kind of evidence (what is known vs. what is actually the case).7 Thelatter difference indicates that we are dealing with two accessibility relations,not one. Must is indeed epistemic, since it takes into consideration what isknown, and should in these examples is not epistemic, since it does not takeinto consideration what is known. We might call it instead a metaphysical

modality:8

it takes all the facts that are actually the case at a particulartime into consideration.Assuming that we adopt this distinction, why then there is a difference

in the direction of inference? Is there any reason why epistemic inferencesproceed from present evidence to past or present events, while metaphysicalinferences proceed from earlier facts to later facts?

Metaphysical causation, the garden-variety causation of one event caus-ing another, requires that the causing event begin earlier than the causedevent. So metaphysical inference is as follows: We infer, given the causingevent, that the caused event happened.9 Epistemic inference seems at firstto be just the opposite: surely there we reason from effect to cause (thewet ground to the raining) instead of the other way around. But in anothersense, we are still inferring from cause to effect, using a different flavor ofcausation. Learning that the ground is wet causes us to conclude that it hasrained, assuming that there is no other relevant information. This kind ofcausation we might term epistemic causation: information causes a certainchange in a belief state, as long as no other information intervenes. This wayof looking at epistemic inference makes it parallel to metaphysical inference,in which an event causes a certain change in the state of the universe, as

7A third difference is whether have scopes over or under the modal. This differencehas been dealt with at length by, for instance, Condoravdi (2001), Stowell (2004), andDemirdache and Uribe-Etxebarria (2005). I will not address it here.

8Kratzer would derive such an accessibility relation from a totally realistic modalbase; the idea is the same. I prefer the term metaphysical because of its use in thephilosophical literature (see Thomason (1970), e.g.) to talk about the future, and becauseof the causal distinction discussed just below.

9Or, in the case of should, that it would have happened if nothing else intervened.

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long as no other events intervene. The directionality of epistemic causation,

from later events to earlier events, then would have to follow from what canbe information, a topic I will not pursue here. In any case, modulo anytype-shifting that a real definition of information might necessitate, wecan maintain the same formal denotation for metaphysical should as we hadfor the epistemic denotation of should, changing only the ordering sourceand modal base. The ordering source changes from highest-plausibility(no other information intervenes, that is, all else is epistemically equal) tohighest-entropy (no other events intervene, that is, all else is metaphysi-cally equal). The modal base changes from what is known (yielding EC,the set of worlds epistemically accessible from C), to what is/has been the

case (yielding MC, the set of worlds metaphysically accessible from C).Additionally, we use the relation more restrictive than rather than moreinformative than.

(26) for all C, p:[[shouldmeta]](C)(p) asserts that highest-entropyC(MC) p, andpresupposes that M more restrictive than MC:Mhighest-entropyC(MC) =

But since more restrictive means later for metaphysical states, we havea problem. If the non-deontic reading of (27) involves metaphysical should,

it ought to mean that according to the current state of affairs, if nothing elsehappens, John is home after the moment of utterance. This is because anymore restrictive metaphysical state must be a later one, because somethinghas to have happened to make it a different metaphysical state. But (27)cannot have that meaning. Instead it conveys that the speaker thinks Johnis home now, not later than now.

(27) John should be at home now.

We could circumvent this problem by replacing more restrictive than withat least as restrictive as, as in (28).

(28) for all C, p:[[shouldmeta]](C)(p) asserts that highest-entropyC(MC) p, andpresupposes that M at least as restrictive as MC:Mhighest-entropyC(MC) =

However, for the case where M = MC, the presupposition would be trivially

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true, which is not what we want.

So perhaps (27) is epistemic after all. Even with should have, which gaveus the original metaphysical example, it is possible to get (28b) to be betterin the context where the ground is wet, with a marked intonation:

(29) I dont understand it. The ground is wet, even the leaves on thetrees are wet, as far as the eye can see. It SHOULD have rained.But youre telling me its just a very sophisticated sprinkler system.

I find the marked intonation to be obligatory here.So epistemic readings of should have do exist, albeit with marked into-

nation. Present-oriented should seems to require an epistemic reading. And

there is indirect evidence that epistemic readings exist for future-orientedshould, with the same marked intonation as for should have. As Leech pointsout, should is a bit weird out of the blue if the eventuality is not one thespeaker desires.

(30) (adapted slightly from Leech 1971, p. 102)

a. Our candidate should win the election.b. Roses should grow pretty well in this soil.c. ?*Our candidate should lose the election.d. ?*Roses should grow pretty badly in this soil.

The weirdness of (30c) and (30d), whatever its cause, goes away when themarked intonation is used:

(31) a. She raised less money than the other candidate, she had a lousycampaign manager, and whats more, shes actually a convictedfelon. Our candidate SHOULD lose the election. Unless some-how all the other candidates supporters stay home.

b. Roses SHOULD grow pretty badly in this soil, but knowinghow serious Jenny is about using the blue stuff, I bet her roseswill do just fine.

Since the marked intonation correlates with the epistemic reading of shouldhave, we may conclude here that it is the epistemic reading of should thatescapes Leechs constraint.10

10Additional evidence for this claim comes from future-oriented epistemic may, whichalso needs the marked intonation:

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So: while not every non-deontic use of should is epistemic, some of them

are.11

This denotation captures what we need for metaphysical should. Be-fore going on to deontic or practical necessity should. we must confirm thatmetaphysical should is weaker than epistemic must, as desired.

To summarize the discussion so far: We have seen that the traditionalanalysis of non-deontic should, based on the idea that should has less-than-universal quantification than epistemic must, erroneously predicts that shouldshould trigger Moores paradox. This led us to develop an alternative theory,in which must, but not should, requires that any later epistemic state turnout not to make p true. This distinction between must and should was calledefficacy, since the issue is whether what is now most plausible actually

(i) a. John MAY leave. epistemic (contrastive deontic also )b. John may LEAVE. *epistemic,

deontic

11Shouldbehaves like mustand maywith respect to epistemic containment (von Finteland Iatridou, 2003). On the epistemic reading of (i), von Fintel and Iatridou note, hiscannot be a bound variable.

(i) #Every student must be home if his light is on.

a. epistemic reading: *b. deontic reading: fine

Epistemic shouldand may, as diagnosed by the marked intonation, also block the variablebinding:

(ii) #Every student MAY be home tomorrow if his light is on.

(iii) #Every student SHOULD be home tomorrow if his light is on.

But even without the marked intontation, the bound variable reading is not possible, asshown by the unacceptability of (iv).

(iv) #Every student should be home tomorrow if his light is on.

This means that our metaphysical shouldalso exhibits epistemic containment. This fact isnot necessarily a problem for the current analysis, however. Even epistemic conditionalswithout overt epistemic modals have the epistemic containment property:

(v) #Every student is at home if his light is on.

Since the sentence in (v) has an epistemic flavor in some sense, but no explicit modal,we have to wonder how exactly the conditional semantics, as separate from the modalsemantics, plays a role; it may play the same role in (iv). But we will have to leave thisquestion here.

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manages to be true.

This theory proved not to be adequate, as some instances ofshouldseemednot to involve epistemic inference at all. In addition to epistemic modality, weintroduced metaphysical modality to account for these cases. The table belowsets out the analogous terms between epistemic and metaphysical modality.12

(32) epistemic metaphysicalmodal base E: set of worlds that M: set of worlds that

agree with what is known agree with what is the caseordering source highest-plausibility highest-entropy

5 Deontic shouldA similar issue of strength and weakness arises for deontic should and must:

(33) a. #You must pay the rent, in fact you should.b. You should pay the rent, in fact, you must.

Does the analysis given above for epistemic and metaphysical should transferto deontic should? Deontics are supposed to have a metaphysical modalbase and an ordering source for the best worlds based on ideals. Suppose weentertain the denotations in (34) (just like the metaphysical denotations, but

highest-contentment is a function that takes a set of worlds and returnsthe subset that best agrees with a salient set of ideals).

(34) for all p, C:

a. [[must]](p)(C) asserts that highest-contentment(MC) p,and presupposes that M more restrictive than MC:(M) highest-contentment(MC)

b. [[should]](p)(C) asserts that highest-contentment(MC) p,and presupposes that M more restrictive than MC:M highest-contentment(MC) =

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It is worth asking whether the difference between may and might is that may has apositive efficacy presupposition, like must, and might has a zero efficacy presupposition,like should. My intuition is that may seems to express possibility given a certain state ofaffairs, while might seems to accept that outside events could intervene.

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The presupposition of (34a) at first looks a bit odd, but it is exactly as

Werner (2005) argues: you do what you gotta do, i.e., must implies will.13

The real problem is with the presupposition in (34b). It says that theset of metaphysically possible worlds at some later time has a non-emptyintersection with the set of worlds that (as of this moment) would bring thehighest-contentment. That is, its still possible that youll actually end upwith a highest-contentment world. This is fine as far as it goes. Leech (1971)for instance says that:

[I]f someone says You must buy some new shoes, it is assumedthat the purchase will be carried out; the tone of must tolerates

little argument. But You should buy some new shoes is a differentmatter the speaker here could well add in an undertone, but Idont know whether you will or not.

It seems to me, however, that the presupposition in (34b) is more appli-cable to be supposed to than to should. Consider the minimal pair in (35):

(35) a. You should buy some new shoes.b. Youre supposed to buy some new shoes.

The be supposed to (bst) sentence in (35b) corresponds quite nicely to (34b).There is a set of ideals,14 which we use to construct a function highest-contentment. A bst p sentence says that all highest-contentment worldsare p worlds, and presupposes only that its possible for the actual world toturn into a p world, not that it will.

The should sentence, however, is a little different. Rather than presup-posing that the salient set of ideals is a set that the interlocutor accepts, thespeaker, if anything, is presupposing only that the interlocutor might acceptthis set of ideals.15 A paraphrase of a deontic should p sentence would thusbe as in (36):

13Note that you dont necessarily do what you should do; Werner specifically excludes

should from his discussion.14Of course bst requires that the ideals be provided by some authority. Im betting thatthat lexical difference is irrelevant to the current discussion.

15Actually, not necessarily the interlocutor. Suppose you are talking to your friendabout Tasha and you say (i).

(i) Tasha should go to bed now.

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(36) Deontic should p: If you accept exactly these ideals, then, assuming

certain laws of rational behavior, p

The rational behavior clause is needed because of course you could behaveirrationally and not do what you want to do. But assuming that you arerational, you will do what you want to do.16

At first look, this paraphrase seems to ruin the parallelism between de-ontic should and the other shoulds. But note that we can restate the othershoulds in a similar way.

(37) a. Metaphysical should: If exactly these facts are true, then, as-suming certain laws of physics, p

b. Epistemic should: If exactly this information is known, then,assuming certain laws of probability, p

These paraphrases have three components:

(38) a. The beginning ideals/facts/informationb. The ceteris paribus condition (exactly these, nothing else inter-

venes)c. The laws of rational behavior/physics/plausibility

This is a slightly different picture from Kratzers theory, which has two com-

ponents:(39) a. Modal base: The beginning facts/information

b. Ordering source: ideals, ceteris paribus, possibly laws of physics,plausibility?

On Kratzers theory, the role the ideals play is in the ordering source. Thatswhat we were assuming when we created highest-plausibility, highest-entropy, and highest-contentment, functions that take a set of worldshanded them by the modal base and return the set of worlds that best agrees

Presumably you mean to say that whoevers in charge of Tashas bedtime, if they accept

the relevant ideals, will make her go to bed. Your interlocutor may or may not be incharge of Tasha, therefore it is not the interlocutor whose ideals matter, but whoever isin charge.

16One issue not resolved by this paraphrase is the fact that deontic should p sentencesare strange if it is impossible for p to happen. So the laws of physics may need to beincluded here; it is not immediately clear to me how to include them.

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with the ideals. So it should be analogous to the laws of physics or probability.

Here, however, it seems as though the ideals are playing the same role theinitial facts are, instead; for Kratzer, that would be the modal base. But onthis theory, the analogies between the three kinds of should would be verysurprising indeed; the ideals need to play the same role as the things thatKratzer put in the modal base.

One good reason to think that this is right is that ideals, like facts andunlike the laws of physics and probability, are particular to particular situa-tions. Whats constant are the laws of rational behavior. That, then, is thetrue analogue to the (nave) laws of physics and the laws of probability. Notethat all of these kinds of laws are deterministic, as long as we know what

ideals, facts, or information we started with.If ideals are in the same basket with things like facts and information, thatbasket must be able to have a set of propositions that yields no consistentset of worlds (this was the initial observation which led to the use of ideals inthe ordering source in the first place). Can this be reconciled with epistemicand metaphysical cases? I think yes. There is no reason to believe thatepistemic modals are not doxastic, with weighted beliefs, just as you mighthave differently-weighted ideals. As for the metaphysical cases, we can thinkof them as including differently-weighted physical forces.

If we accept this kind of story, we will have to jettison all the denotationswe have given so far for modals, since they are predicated on the modalbase/ordering source picture. More details need to be worked out, and thereis no space to do it here, but here is a sketch of the formal elements of themeaning ofshouldand must, to be treated as a starting point for future work.

Instead of a modal base, there is a situation argument, a set of propo-sitions: everything that goes into a modal base, and ideals as well, all thethings that are particular to the actual time and place. If f is a functionthat takes a situation and applies the relevant natural laws to it, the generalassertion of all flavors of must and should is simply:

(40) p s . p(f(s))

By choosing the situation argument appropriately, and choosing the naturallaws appropriately, the different flavors are generated.17

17While it is not immediately clear how (40) might be extended to deal with may andmight, since we are no longer quantifying over possible worlds, it could be done. Onemight take a subpart of the situation argument to be the argument for f, for example.

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The presuppositions are harder to state, but an informal shot at them is

given in (41):

(41) a. presupposition ofmust: the salient situation s* is exactly whatmatters (no other facts/ideals enter in)

b. presupposition of should: the salient situation s* may or maynot be exactly what matters (other facts/ideals may enter in)

With this admittedly unfinished suggestion we must stop and leave the detailsfor future work.

6 What we should concludeThis discussion has generated three heuristics for further research on thesemantics of modals.

Relative strength isnt always relative quantificational force;

sometimes its efficacy. Recall that the traditional theory ofshould, whereit had a Most quantifier, was unsatisfying. I suspect that quantifiers like mostplay no role in modal semantics, and would hypothesize that relative weak-ness can always be explained by (a) the difference between existential anduniversal quantification, (b) whether the actual world is presupposed to beinertial or not (efficacy), and/or (c) how the quantificational set is selected.

Thus, if a speaker of a language tells you that one modal sentence makes astronger claim than another modal sentence, all you can conclude is thatthere is more work to be done.

Inference from evidence isnt always epistemic modality; some-

times its metaphysical modality. While it seemed obvious that non-deontic uses of should were epistemic in nature, that turned out not alwaysto be the case. There are two different ways of making an inference. Epis-temic inference can go backwards in time; metaphysical inference does not.Therefore, if a speaker of a language tells you that a modal sentence involvessome evidence for a claim, you still need to find out if it is epistemic or

metaphysical inference (or conceivably something else).We should reconsider modal bases and ordering sources, at

least as they are currently understood. In trying to extend the analysisto deontic should, we saw that we needed to reconsider the role played byideals, and thereby to reconsider the basic framework of modal semantics.Kratzers theory of modality has brought us a very long way indeed, but it

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would benefit from a re-division of labor along the lines sketched above.

References

Barwise, J. and R. Cooper (1981). Generalized quantifiers and natural lan-guage. Linguistics and Philosophy 4 (2), 159210.

Beaver, D. (2001). Presupposition and Assertion in Dynamic Semantics.Oxford: CSLI and folli.

Condoravdi, C. (2001). Temporal interpretation of modals. In D. Beaver,S. Kaufmann, B. Clark, and L. Casillas (Eds.), Stanford Papers on Seman-tics. Palo Alto: CSLI Publications.

Copley, B. (2002). The Semantics of the Future. Ph. D. thesis, MIT. Toappear, Outstanding Dissertations in Linguistics, Routledge.

Demirdache, H. and M. Uribe-Etxebarria (2005). On the temporal syntax ofnon-root modals: Covaluation, binding, and scope reversal. Talk presentedat the Paris Time and Modality International Roundtable.

von Fintel, K. and S. Iatridou (2003). Epistemic containment. LinguisticInquiry 34 (2), 173198.

Horn, L. R. (1989). A Natural History of Negation. University of ChicagoPress.

Kratzer, A. (1991). Modality. In A. von Stechow and D. Wunderlich (Eds.),

Semantics: An International Handbook of Contemporary Research. Berlin:de Gruyter.

Leech, G. N. (1971). Meaning and the English Verb. Essex, U.K.: LongmanGroup Limited.

Lewis, D. (1968). On the Plurality of Worlds. Oxford: Basil Blackwell.Lewis, D. (1975). Counterfactuals. Cambridge, Mass.: Harvard University

Press.Stowell, T. (2004). Tense and modals. In J. Gueron and J. Lecarme (Eds.),

The Syntax of Time, pp. 621636. Cambridge, Mass.: MIT Press.Thomason, R. (1970). Indeterminist time and truth-value gaps. Theoria 36,

264281.Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical

Logic 25(3), 221261.Werner, T. (2005). You do what you gotta do, or why must implies will. In

Proceedings of SALT 15.

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